Question

What is the derivative of `xe^x`?

Answer 1

`(x+1)e^x`

Explanation:

From product rule,

`d/dx[xe^x]=x*d/dxe^x+e^x*d/dxx`

`=xe^x+e^x`

Answer 2

`e^x (x+1)`

Explanation:

differentiate using `color(blue)(" product rule ")`

`d/dx(xe^x) = x d/dx(e^x) + e^x d/dx (x)`

[now `d/dx(e^x) = e^x`]

`rArr d/dx(xe^x) = xe^x + e^x = e^x( x + 1 )`